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What Determines the Breakup Length of a Jet?

Stefan Kooij1, Daniel T. A. Jordan2, Cees J. M. van Rijn1, Neil M. Ribe3, and Daniel Bonn1

Phys. Rev. Lett. 135, 214001 – Published 17 November, 2025

DOI: https://doi.org/10.1103/jf6w-l5sy

Abstract

The breakup of a capillary jet into drops is believed to be governed by initial disturbances on the surface of the jet that grow exponentially. The disturbances are often assumed to be due to external sources of noise, to turbulence, or to imperfections of the nozzle. Here we demonstrate that the initial disturbances observed across a wide range of conditions are quantitatively consistent with thermal capillary waves, where the initiating disturbances must be of the order of an angstrom, suggesting that thermal noise can act as a primary driver of jet breakup under typical experimental conditions. Our experiments with a wide range of nozzles show no significant variation in breakup length linked to nozzle type, shape, or inner roughness. By systematically varying the jet diameter and velocity and the fluid properties, we validate our thermal disturbance model over 4 orders of magnitude in jet length, and 7 orders of magnitude when previous molecular dynamics simulations and stochastic hydrodynamics calculations of nanojets are included.

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References (25)

  1. D. Lohse, Fundamental fluid dynamics challenges in inkjet printing, Annu. Rev. Fluid Mech. 54, 349 (2022).
  2. M. X. Zhang, F. Verhoeven, P. Ravensbergen, S. Kooij, R. Geoffrion, D. Bonn, and C. J. van Rijn, Improved olfactory deposition of theophylline using a nanotech soft mist nozzle chip, Pharmaceutics 16, 2 (2023).
  3. D. D’Angelo, S. Kooij, F. Verhoeven, F. Sonvico, and C. van Rijn, Fluorescence-enabled evaluation of nasal tract deposition and coverage of pharmaceutical formulations in a silicone nasal cast using an innovative spray device, J. Advert. Res. 44, 227 (2023).
  4. A. Ziaee, A. B. Albadarin, L. Padrela, T. Femmer, E. O’Reilly, and G. Walker, Spray drying of pharmaceuticals and biopharmaceuticals: Critical parameters and experimental process optimization approaches, Eur. J. Pharm. Sci. 127, 300 (2019).
  5. A. Gharsallaoui, G. Roudaut, O. Chambin, A. Voilley, and R. Saurel, Applications of spray-drying in microencapsulation of food ingredients: An overview, Food Res. Int. 40, 1107 (2007).
  6. J. Eggers and E. Villermaux, Physics of liquid jets, Rep. Prog. Phys. 71, 036601 (2008).
  7. L. Rayleigh, On the capillary phenomena of jets, Proc. R. Soc. London 29, 71 (1879).
  8. C. Weber, Zum zerfall eines flüssigkeitsstrahles, ZAMM-J. Appl. Math. Mech./Z. Angew. Math. Mech. 11, 136 (1931).
  9. R. E. Phinney, Stability of a laminar viscous jet–the influence of the initial disturbance level, AIChE J. 18, 432 (1972).
  10. R. J. Donnelly and W. Glaberson, Experiments on the capillary instability of a liquid jet, Proc. R. Soc. A 290, 547 (1966).
  11. D. Rutland and G. Jameson, A non-linear effect in the capillary instability of liquid jets, J. Fluid Mech. 46, 267 (1971).
  12. T. A. Kowalewski, On the separation of droplets from a liquid jet, Fluid Dyn. Res. 17, 121 (1996).
  13. A. M. Gañán-Calvo, H. N. Chapman, M. Heymann, M. O. Wiedorn, J. Knoska, B. Gañán-Riesco, J. M. López-Herrera, F. Cruz-Mazo, M. A. Herrada, J. M. Montanero et al., The natural breakup length of a steady capillary jet: Application to serial femtosecond crystallography, Crystals 11, 990 (2021).
  14. C. Zhao, D. A. Lockerby, and J. E. Sprittles, Dynamics of liquid nanothreads: Fluctuation-driven instability and rupture, Phys. Rev. Fluids 5, 044201 (2020).
  15. B. Barker, J. B. Bell, and A. L. Garcia, Fluctuating hydrodynamics and the Rayleigh–Plateau instability, Proc. Natl. Acad. Sci. U.S.A. 120, e2306088120 (2023).
  16. M. Moseler and U. Landman, Formation, stability, and breakup of nanojets, Science 289, 1165 (2000).
  17. F. Savart, Mémoire sur la constitution des veines liquides lancées par des orifices circulaires en mince paroi, Ann. Chim. (Paris) 53, 337 (1833).
  18. P. Lafrance and R. C. Ritter, Capillary breakup of a liquid jet with a random initial perturbation, J. Appl. Mech. 44, 385 (1977).
  19. M.-C. Yuen, Non-linear capillary instability of a liquid jet, J. Fluid Mech. 33, 151 (1968).
  20. D. F. Rutland and G. J. Jameson, A non-linear effect in the capillary instability of liquid jets, J. Fluid Mech. 46, 267 (1971).
  21. H. González, J. Arcenegui, F. J. García de Bollullos, J. R. Castrejón-Pita, and A. A. Castrejón-Pita, Self-stimulated capillary jet, Phys. Rev. Appl. 15, 014054 (2021).
  22. A. Umemura, Self-destabilizing mechanism of a laminar inviscid liquid jet issuing from a circular nozzle, Phys. Rev. E 83, 046307 (2011).
  23. Y. Zhang, J. Sprittles, and D. Lockerby, Thermal capillary wave growth and surface roughening of nanoscale liquid films, J. Fluid Mech. 915, A135 (2021).
  24. R. M. P. Tanyag, A. J. Feinberg, S. M. O. O’Connell, and A. F. Vilesov, Disintegration of diminutive liquid helium jets in vacuum, J. Chem. Phys. 152, 234306 (2020).
  25. Y. Hennequin, D. G. A. L. Aarts, J. H. van der Wiel, G. Wegdam, J. Eggers, H. N. Lekkerkerker, and D. Bonn, Drop formation by thermal fluctuations at an ultralow surface tension, Phys. Rev. Lett. 97, 244502 (2006).

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